A Numerical Algorithm Based On Natural Boundary Naturalization For Quasilinear Problems

In this thesis,based on the principle of natural boundary reduction,the boundary value problems of quasilinear equations on rectangular and elliptic concave regions are studied,and the contents are as follows:In the first chapter,the research progress of natural boundary element method and the related mathematical theory are introduced.In chapter two,the nonoverlapping domain decomposition algorithm(DtN alternating algorithm)is used to study the quasilinear equations in the long strip region.The natural integral equation on the elliptical artificial boundary is obtained by applying the boundary reduction principle,and the corresponding iterative algorithm is constructed.According to the characteristics of nonlinear operators,the convergence of the algorithm in continuous and discrete cases is proved,and the corresponding numerical examples are given to illustrate the feasibility of the method.In chapter three,the coupling of natural boundary element and finite element method is used to study the quasilinear problem in the elliptical concave region,and the natural integral equation on the artificial boundary of elliptic arc is obtained by applying the boundary reduction principle.Meanwhile,we prove the constringency of the coupled variational problem and the convergence of the approximate solution.Finally,a numerical example is given to illustrate the feasibility and effectiveness of the method.